MIMO decoding

ABSTRACT

In MIMO wireless communications employing LMMSE receiver, the symbols transmitted through a transmit antenna are estimated at the receiver in the presence of interference consisting of two main components: one due to the additive noise and the other due to (interfering) symbols transmitted via the remaining antennas. This has been shown to hamper the performance of a communication system resulting in incorrect symbol decisions, particularly at low SNR. IMMSE has been devised as a solution to cope with this problem; In IMMSE processing, the symbols sent via each transmit antenna are decoded iteratively. In each stage of processing, the received signal is updated by removing the contribution of symbols detected in the previous iterations. In principle, this reduces the additive interference in which the desired symbols are embedded in. Therefore, the interference level should reduce monotonically as one goes down in processing order. In a noisy environment, however, any incorrect decision made on a symbol in an iteration leaves its contribution in the updated received signal available for processing in the following iterations. Fortunately, if the level of interference is estimated and the soft bits are scaled appropriately by the estimated interference power, the performance of IMMSE receiver can be greatly improved. Preferred embodiments estimate the interference by computing the probability of error in decoding the symbols of the previous stage(s). The computation of decision error probability depends on the constellation size of transmitted symbols and introduces very little processing overhead.

CROSS-REFERENCE TO RELATED APPLICATIONS

The following applications disclose related subject matter and have acommon assignee with the present application: application Ser. No.10/765,009, filed Jan. 26, 2004, now U.S. Pat. No. 7,321,564.

BACKGROUND OF THE INVENTION

The present invention relates to communication systems, and moreparticularly to multiple-input multiple-output wireless systems.

Wireless communication systems typically use band-limited channels withtime-varying (unknown) distortion and may have multi-users (such asmultiple clients in a wireless LAN). This leads to intersymbolinterference and multi-user interference, and requiresinterference-resistant detection for systems which are interferencelimited. Interference-limited systems include multi-antenna systems withmulti-stream or space-time coding which have spatial interference,multi-tone systems, TDMA systems having frequency selective channelswith long impulse responses leading to intersymbol interference, CDMAsystems with multi-user interference arising from loss of orthogonalityof spreading codes, high data rate CDMA which in addition to multi-userinterference also has intersymbol interference.

Interference-resistant detectors commonly invoke one of three types ofequalization to combat the interference: maximum likelihood sequenceestimation, (adaptive) linear filtering, and decision-feedbackequalization. However, maximum likelihood sequence estimation hasproblems including impractically large computation complexity forsystems with multiple transmit antennas and multiple receive antennas.Linear filtering equalization, such as linear zero-forcing and linearminimum square error equalization, has low computational complexity buthas relatively poor performance due to excessive noise enhancement. Thedecision-feedback (iterative) detectors, such as iterative zero-forcingand iterative minimum mean square error, have moderate computationalcomplexity and exhibits superior performance compared to linearreceivers.

In an iterative receiver, the symbols from a transmit antenna are firstdetected. The contribution due to these symbols in the received signalis then removed, followed by detection of symbols from the secondtransmit antenna. This procedure is followed until all transmittedsymbols are detected. Since the soft symbols and soft bits are estimatedin the presence of noise, they have to be scaled appropriately beforebeing fed into the Viterbi decoder for the recovery of transmitted bits.

SUMMARY OF THE INVENTION

The present invention provides methods and detectors for multiple-inputmultiple-output (MIMO) systems with interference cancellation by aadjusting the scaling of soft estimates depending upon interferencecancellation error probabilities.

This has shown advantages including improved performance for wirelesssystems.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow diagram.

FIGS. 2 a-2 c illustrate functional blocks of detectors, receivers, andtransmitters.

FIGS. 3 a-3 b show 2×2 MIMO OFDM transmitter and receiver.

FIG. 4 illustrates simulation results.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

1. Overview

Preferred embodiment detectors and detection methods for multi-input,multi-output (MIMO) systems with interference cancellation capabilitiescompensate for decision errors in the symbols for cancellation byadjusting the scaling (normalization) of the transmitted soft symbol.The scaling factor has additive interference term proportional to aparameter depending upon the probability of decision errors. FIG. 1 is aflow diagram for a first preferred embodiment method with the additiveinterference term proportional to an estimate of the mean squaredecision error.

Preferred embodiment communication systems, such as wireless local areanetworks, include preferred embodiment interference cancellationreceivers employing preferred embodiment interference cancellationmethods. The computations can be performed with digital signalprocessors (DSPs) or general-purpose programmable processors orapplication specific circuitry (ASICs) or systems on a chip such as botha DSP, ASIC, and RISC processor on the same chip with the RISC processorin control. Analog-to-digital converters and digital-to-analogconverters provide coupling to the real world, and modulators anddemodulators (plus antennas for air interfaces) provide coupling fortransmission waveforms.

2. Single Stage Iterative MMSE Detectors

FIG. 2 a illustrates a generic MIMO transmitter, and FIG. 2 billustrates a MIMO receiver with an interference-resistant detector;these could be part of a wireless communications system with P transmitantennas (P data streams) and Q receive antennas. The received signal insuch a system can be written as:r=H s+wwhere r is the Q-vector of samples of the received baseband signal(complex numbers) corresponding to a transmission time n:

${r = \begin{bmatrix}{r_{1}(n)} \\{r_{2}(n)} \\\vdots \\{r_{Q}(n)}\end{bmatrix}};$s is the P-vector of transmitted symbols (sets of complex numbers of asymbol constellation) for time n:

${s = \begin{bmatrix}{s_{1}(n)} \\{s_{2}(n)} \\\vdots \\{s_{P}(n)}\end{bmatrix}};$H is the Q×P channel matrix of attenuations and phase shifts; and w is aQ-vector of samples of received (white) noise. That is, the (q,p)thelement of H is the channel (including multipath combining andequalization) from the pth transmit source to the qth receive sink, andthe qth element of w is the noise seen at the qth receive sink.

Note that the foregoing relation applies generally to various systemswith various interference problems and in which n, r, s, P, and Q havecorresponding interpretations. For example:

-   (i) High data rate a multi-antenna systems such as BLAST (Bell Labs    layered space time architecture) or MIMO and multi-stream space-time    coding: spatial interference suppression techniques are used in    detection.-   (ii) Broadband wireless systems employing OFDM (orthogonal frequency    division multiplex) signaling and MIMO techniques for each tone or    across tones.-   (iii) TDMA (time division multiple access) systems having    frequency-selective channels with long impulse response which causes    severe ISI (intersymbol interference). Use equalizers to mitigate    ISI.-   (iv) CDMA (code division multiple access) systems having    frequency-selective channels which cause MUI (multi-user    interference) as a result of the loss of orthogonality between    spreading codes. For high data rate CDMA systems such as HSDPA and    1×EV-DV, this problem is more severe due to the presence of ISI.    Equalizers and/or interference cancellation may be used to mitigate    these impairments.-   (v) Combinations of foregoing.

P is essentially the number of symbols that are jointly detected as theyinterfere with one another, and Q is simply the number of collectedsamples at the receiver. Because there are P independent sources, Q mustbe at least be as large as P to separate the P symbols. A detector in areceiver as in FIGS. 2 a-2 b outputs soft estimates z of the transmittedsymbols s to a demodulator and decoder.

Presume that different symbols that are transmitted via P differentantennas are uncorrelated and may also utilize different modulationschemes. This implies the P×P matrix of expected symbol correlations,Λ=E[ss^(H)], is diagonal with entries equal the expected symbol energies(λ_(k)=E[|s_(k)|²]); i.e.,

$\Lambda = \begin{bmatrix}\lambda_{1} & 0 & \cdots & 0 \\0 & \lambda_{2} & \cdots & 0 \\\vdots & \vdots & ⋰ & \vdots \\0 & 0 & \cdots & \lambda_{P}\end{bmatrix}$

For linear filtering equalization detectors, such as linear zero-forcing(LZF) or linear minimum mean square error (LMMSE), the soft estimates,denoted by P-vector z, derive from the received signal by linearfiltering with P×Q matrix F; namely, z=F r. LZF detection essentiallytakes F to be the pseudoinverse of H; namely, F=[H^(H)H]⁻¹H^(H).

In contrast, LMMSE detection finds the matrix F by minimizing the meansquare error, E[∥z−s∥²]. With perfect estimation of the channel H, theminimizing matrix F is given by:

F = [H^(H)H + σ²Λ⁻¹]⁻¹H^(H) = Λ H^(H)[H Λ H^(H) + σ²I_(Q)]⁻¹where σ² is the variance per symbol of the additive white noise w andI_(Q) is the Q×Q identity matrix. Note F has the form of a product of anequalization matrix with H^(H) which is the matrix of the matched filterfor the channel. Also, note that this LMMSE detector is biased; however,the normalization (scaling) can correct this as described below andindicated in FIG. 2 b.

A one-stage iterative (decision-feedback) detector for blocks of Psymbols has a series of P linear detectors (P iterations) with eachlinear detector followed by a (hard) decision device and interferencesubtraction (cancellation). Each of the P linear detectors (iterations)generates both a hard and a soft estimate for one of the P symbols. Thehard estimate is used to regenerate the interference arising from thealready-estimated symbols which is then subtracted from the receivedsignal, and the difference used for the next linear symbol estimation.This presumes error-free decision feedback. More explicitly, let sdenote the P-vector of transmitted symbols to be estimated, ŝ^((i))denote the ith iteration output P-vector of hard symbol estimates (firsti components equal to the hard estimates ŝ₁, ŝ₂, . . . , ŝ_(i) of thefirst i symbols, s₁, s₂, . . . , s_(i), and the remaining P−i componentseach equal to 0), and z^((i)) denote the ith iteration output P-vectorof soft estimates of s₁−ŝ₁, s₂−ŝ₂, . . . , s_(i−1)−ŝ_(i−1), s_(i),s_(i+1), . . . , s_(P). That is, estimates of the transmitted symbolswith the already-estimated first i−1 symbols subtracted out. The harddecision for the ith symbol, ŝ_(i), arises from application of a harddecision operator on the soft estimate: ŝ_(i)=D{z_(i) ^((i))}. The ithiteration detection is:z ^((i)) =F r−F H ŝ ^((i−1))where the second term is the soft estimation of the regenerated(propagated by H) hard decision symbol estimates of the prior i−1iterations. For the first iteration there are no already-estimatedsymbols, so take ŝ⁽⁰⁾=0_(P), a P-vector with each component equal to 0.Ideally, for the ith iteration the soft estimates z₁ ^((i)), z₂ ^((i)),. . . , z_(i−1) ^((i)) are just estimates of channel noise because thehard estimates would exactly cancel the transmitted symbols. Thuscomputational simplicity suggests omitting these computations byzeroing-out the corresponding rows (columns) of the matrices. Moreprecisely, take:z ^((i)) =F ^((i)) r−G ^((i)) ŝ ^((i−1))where F^((i)) and G^((i)) are the P×Q detection matrix and the P×Pinterference cancellation matrix for the ith iteration, respectively,and defined as:

$F^{(i)} = \begin{bmatrix}0_{{({i - 1})}{xQ}} \\\Phi^{(i)}\end{bmatrix}$ $G^{(i)} = {F^{(i)}\left\lfloor \begin{matrix}B_{i - 1} & \left. 0_{{Qx}{({P - i + 1})}} \right\rfloor\end{matrix} \right.}$where the inversion matrix for IMMSE is

$\begin{matrix}{\Phi^{(i)} = {\left( {{A_{i}^{H}A_{i}} + {\sigma^{2}\Lambda_{i}^{- 1}}} \right)^{- 1}A_{i}^{H}}} \\{= {\Lambda_{i}{A_{i}^{H}\left( {{A_{i}\Lambda_{i}A_{i}^{H}} + {\sigma^{2}I_{Q}}} \right)}^{- 1}}}\end{matrix}$Here the last P−i+1 and first i−1 symbol portions of the channel matrixH are defined in terms of the P column vectors h₁, h₂, . . . , h_(P) ofH as:A_(i)=[h_(i), h_(i+1), . . . , h_(P)]a Q×(P−i+1) matrix, andB_(i)=[h₁, h₂, . . . , h_(i−1)]a Q×(i−1) matrix. Also, 0_((i−1)×Q) is the (i−1)×Q matrix of 0s,0_(Q×(P−i+1)) is the Q×(P−i+1) matrix of 0s, and Λ_(i) is thelower-right (P−i+1)×(P−i+1) diagonal submatrix of Λ and thus the symbolenergies of the symbols not-already estimated. FIG. 2 c illustratesiterative detection.

Ordered detection based on the symbol post-detectionsignal-to-interference-plus-noise ratio (SINR) is often used to reducethe effect of decision feedback error. In particular, let the detectionorder be π(1), π(2), . . . , π(P) where π( ) is a permutation of the Pintegers {1, 2, . . . , P}; that is, the first estimated symbol (hardestimate output) will be ŝ_(π(1)) and thus also be the correspondingnonzero element of ŝ⁽¹⁾. The maximum SINR of the components of the firstsoft estimate z⁽¹⁾, which estimates all P symbols, determines π(1).Similarly, the SINRs of the components of z⁽²⁾, which estimates all ofthe symbols except the cancelled s_(π(1)), determines π(2), and soforth. That is, the ith iteration estimates symbol s_(π(i)), andmodifying the foregoing to accommodate the ordering is routine butomitted for clarity in notation. Indeed, simply denote the resulting Psoft symbol estimates as z₁, z₂, . . . , z_(P). These MMSE detectors arebiased estimators in the sense that E[z_(k)|s_(k)]−s_(k)≠0. However, thebias of the MMSE detectors can be removed by applying a scaling factorto the soft outputs. This scaling factor does not affect post-detectionSINR, yet results in increased mean square error compared to the regularbiased MMSE estimate. While this unbiasing operation does not affect theperformance of LMMSE detectors, it improves the performance of IMMSEdetectors because the decision device that is used to generate decisionfeedback assumes unbiased soft output. The unbiasing operation for IMMSEdetectors rescales the soft estimates as follows:

${\overset{ˇ}{z}}_{k} = {z_{k}/v_{k}}$ wherev_(k) = λ_(k)h_(k)^(H)[A_(k)Λ_(k)A_(k)^(H) + σ²I_(Q)]⁻¹h_(k)   = ([A_(k)^(H)A_(k) + σ²Λ_(k)⁻¹]⁻¹A_(k)^(H)A_(k))_(1, 1)with {circumflex over (z)}_(k) denoting the soft output after unbiasingand the subscript 1,1 denoting the (1,1) matrix element. For unbiasedIMMSE, variance-based and mean-squared-error-based normalizations areequivalent.

For a channel encoder (see FIG. 2 a) using a convolution code, thedemodulator (see FIG. 2 b) converts the output P soft symbol estimates,z₁, z₂, . . . , z_(P), into (bit-level) conditional probabilities of thetransmitted symbols, s₁, s₂, . . . , s_(P); and a decoder may translate(using a channel model) the conditional probabilities into branch metricvalues for trellis path searching. In particular, a maximum likelihood(Viterbi) decoder may use a branch metric derived from bit-levelversions of log{p(z|s)}, whereas a Fano algorithm sequential decoder mayuse a branch metric from bit-level versions of log{p(z|s)/p(z)}−K whereK is the log₂ of the number of possible inputs. For a channel encoderusing a turbo code, the demodulator may provide log-likelihood ratioslike log{p(b=0|z)/p(b=1|z)} to an iterative MAP decoder. Of course, ahard decision decoder just directly converts the soft symbol estimatesinto hard symbol estimates.

For example, an AWGN channel where the residual interference(interference which is not cancelled) is also a zero-mean,normally-distributed, independent random variable, gives:p(z _(k) |s _(k) =c)˜exp(−|z _(k) −c| ²/γ_(k))where c is a symbol in the symbol constellation and γ_(k) is anormalization (scaling) typically derived from the channelcharacteristics and the detector type. Of course, γ_(k) is just twicethe variance of the estimation error random variable.

For LZF type detectors the natural choice of γ_(p) is the variance ofthe noise term associated with the soft estimate; that is,γ_(p)=var(n_(p)) where z_(p)=s_(p)+n_(p). This relates to the AWGN noisepower of the channel (σ²) and the corresponding (p,p) diagonal term ofthe matrix which amplifies the channel noise:γ_(p)=σ² [H ^(H) H]⁻¹ _(p,p)And for the iterative ZF detector (with numerical ordering) the analogapplies:γ_(p)=σ² [A _(p) ^(H) A _(p)]⁻¹ _(1,1)where the (1,1) element corresponds to the channel from the pth symbolsource due to the definition of A_(p) with first column equal h_(p).

For MMSE-type detectors a natural choice is to take γ_(p) as the meansquare error:γ_(p) =E[|z _(p) −s _(p)|²]For LMMSE this translates toγ_(p)=σ² [H ^(H) H+σ ²Λ⁻¹]⁻¹ _(p,p)and for the unordered iterative MMSE the analog obtains:γ_(p)=σ² [A _(p) ^(H) A _(p)+σ²Λ_(p) ⁻¹]⁻¹ _(1,1)MMSE-type detectors can also use a variance type normalization.

Because MMSE detectors are biased in the sense that the mean of theestimation error, E[z_(p)−s_(p)], is not zero, the variancenormalization becomesγ_(p) =E[|z _(p) −s _(p)|² ]−|E[z _(p) −s _(p)]|².For linear MMSE this isγ_(p)=σ²([H ^(H) H+σ ²Λ⁻¹]⁻¹ H ^(H) H[H ^(H) H+σ ²Λ⁻¹]⁻¹)_(p,p)and for unordered iterative MMSE this is:γ_(p)=σ²([A _(p) ^(H) A _(p)+σ²Λ_(p) ⁻¹]⁻¹ A _(p) ^(H) A _(p) [A _(p)^(H) A _(p)+σ²Λ_(p) ⁻¹]⁻¹)_(1,1)The bias of the MMSE detectors can be removed as previously described,and for unbiased detectors the mean-square-error normalization and thevariance normalization are thus equivalent.

An alternative normalization simply takesγ_(p)=σ²/(λ_(p) ∥h _(p)∥²) for p=1, 2, . . . , Pwhere ∥h_(p)∥² is the square of the norm of the channel Q-vector h_(p),that is, the sum of the squared magnitudes of the Q components of thepth column of channel matrix H.

In more detail, in terms of the bits b_(kj) which define the symbols_(k) in its constellation (e.g., two bits for a QPSK symbol, four bitsfor a 16QAM symbol, etc.), take as a practical approximationp(z_(k)|b_(kj)=1)=p(z_(k)|s_(k)=c_(kj=1)) where c_(kj=1) is the symbolin the sub-constellation of symbols with jth bit equal 1 and which isthe closest to z_(k); that is, c_(kj=1) minimizes |z_(k)−c_(j=1)|² forc_(j=1) a symbol in the sub-constellation with jth bit equal to 1.Analogously for p(z_(k)|b_(kj)=0) using the sub-constellation of symbolswith jth bit equal 0.

Similarly, the decoder for a binary trellis may use log likelihoodratios (LLRs) which are defined as

$\begin{matrix}{{{LLR}\left( b_{kj} \right)} = {\log\left\{ {{p\left\lbrack {b_{kj} = {1❘z_{k}}} \right\rbrack}/{p\left\lbrack {b_{kj} = {0❘z_{k}}} \right\rbrack}} \right\}}} \\{= {{\log\left\{ {p\left\lbrack {b_{kj} = {1❘z_{k}}} \right\rbrack} \right\}} - {\log\left\{ {p\left\lbrack {b_{kj} = {0❘z_{k}}} \right\rbrack} \right\}}}} \\{= {{\log\left\{ {{p\left( {\left. z_{k} \middle| b_{kj} \right. = 1} \right)}/{p\left( {\left. z_{k} \middle| b_{kj} \right. = 0} \right)}} \right\}} +}} \\{\log\left\{ {{p\left\lbrack {b_{kj} = 1} \right\rbrack}/{p\left\lbrack {b_{kj} = 0} \right\rbrack}} \right\}}\end{matrix}$where the first log term includes the probability distribution of thedemodulated symbol z_(k) which can be computed using the channel model.The second log term is the log of the ratio of a priori probabilities ofthe bit values and typically equals 0. Then again using theapproximation p(z_(k)|b_(kj)=1)=p(z_(k)|s_(k)=c_(kj=1)) where c_(kj=1)is the symbol in the sub-constellation of symbols with jth bit equal 1and which is the closest to z_(k) together with equal a prioriprobabilities yields:

$\begin{matrix}{{{LLR}\left( b_{kj} \right)} = {\log\left\{ {{p\left( {{z_{k}❘b_{kj}} = 1} \right)}/{p\left( {{z_{k}❘b_{kj}} = 0} \right)}} \right\}}} \\{\cong {{1/\gamma_{k}}\left\{ {{\min_{j = 0}{{z_{k} - c_{j = 0}}}^{2}} - {\min_{j = 1}{{z_{k} - c_{j = 1}}}^{2}}} \right\}}}\end{matrix}$Thus the LLR computation just searches over the two symbolsub-constellations for the minima. The magnitude of LLR(b_(kj))indicates the reliability of the hard decision b_(kj)=0 whenLLR(b_(kj))<0 and b_(kj)=1 when LLR(b_(kj))≧0.

The LLRs are used in decoders for error correcting codes such as Turbocodes (e.g., iterative interleaved MAP decoders with BCJR or SOVAalgorithm using LLRs for each MAP) and convolutional codes (e.g. Viterbidecoders). Such decoders require soft bit statistics (in terms of LLR)from the detector to achieve their maximum performance (hard bitstatistics with Hamming instead of Euclidean metrics can also be usedbut result in approximately 3 dB loss). Alternatively, direct symboldecoding with LLRs as the conditional probability minus the a prioriprobability could be used.

3. 2×2 OFDM System First Preferred Embodiment Scalings

First preferred embodiment methods of compensation forinterference-cancellation decision error apply generally to theforegoing MIMO systems, but the methods will be described in terms of anorthogonal frequency division multiplex (OFDM) system with a two-antennatransmitter and a two-antenna receiver as illustrated in FIGS. 3 a-3 b.Such a system could be part of a wireless LAN. In particular, the IEEE802.11 standards include a 20 MHz channel (center frequency about 2.4 or5 GHz) containing 64 equispaced distinct tones with a separation of0.3125 MHz between adjacent tones, and each tone is modulated (e.g.,BPSK, QPSK, 16 QAM, 64 QAM). An IFFT combines the modulated tones fortransmission as illustrated in FIG. 3 a; the symbol interval of 4 μs(microseconds) has 3.2 μs for the data signal and 0.8 μs of guardinterval to lessen interference. 48 of the 64 tones are used as datatones, 4 are used as pilot tones, and 12 are unused; and the set of 48complex numbers corresponding to the data tone modulations constitutesan OFDM symbol. The 4 pilot tones enable the system to track variationsin phase and frequency over the duration of a data packet (e.g., 1000symbols). The 12 unused tones limit interference with adjacent channels.The inverse discrete Fourier transform converts the 64 complex tonemodulations into a 64-sample complex time-domain signal fortransmission: each complex sample maps to in-phase and quadraturewaveforms.

The forward error correction (FEC) coding may be a packet-basedconvolution code with a memory length of 7 (i.e., 64 states) such as thePBCC of the 802.11 standards. A packet preamble (direct sequence spreadspectrum) of 96 μs allows time for estimation of channel parameters(sent to the decoder) during synchronization and training. The FFT ofthe receiver separates the tones, and each tone has a corresponding setof channel parameters (i.e., h₁₁(k), h₁₂(k), h₂₁(k), and h₂₂(k)). Thatis, for the kth tone the received baseband signals from antennas 1 and 2are (with the time dependence omitted) r₁(k) and r₂(k), respectively,and are given by

$\begin{bmatrix}{r_{1}(k)} \\{r_{2}(k)}\end{bmatrix} = {{\begin{bmatrix}{h_{11}(k)} & {h_{21}(k)} \\{h_{12}(k)} & {h_{22}(k)}\end{bmatrix}\begin{bmatrix}{s_{1}(k)} \\{s_{2}(k)}\end{bmatrix}} + \begin{bmatrix}{n_{1}(k)} \\{n_{2}(k)}\end{bmatrix}}$where the kth tone symbol (e.g., point of the constellation) s₁(k) wasfrom transmitter antenna 1, symbol s₂(k) from transmitter antenna 2, andwith corresponding received noise n₁(k) and n₂(k). This can also bewritten in terms of 2-vectors as:r(k)=h ₁(k)s ₁(k)+h ₂(k)s ₂(k)+n(k)where

${h_{j}(k)} = \begin{bmatrix}{h_{j\; 1}(k)} \\{h_{j\; 2}(k)}\end{bmatrix}$is the subchannel from the jth antenna to the two receiver antennas forthe kth tone.

The detector generates soft estimates z₁(k) and z₂(k) for each tone(such as by LZF or LMMSE) and for each tone selects the symbol estimatewith the larger SINR to be used for cancellation and re-estimation ofthe other symbol. In particular, consider LMMSE detection with the 2×2detection matrix F⁽¹⁾ of section 2 and, after unbiasing, express thedetection as weights W_(j,k)*:

$\begin{bmatrix}{z_{1}(k)} \\{z_{2}(k)}\end{bmatrix} = {\begin{bmatrix}{w_{1,1}(k)}^{*} & {w_{1,2}(k)}^{*} \\{w_{2,1}(k)}^{*} & {w_{2,2}(k)}^{*}\end{bmatrix}\begin{bmatrix}{r_{1}(k)} \\{r_{2}(k)}\end{bmatrix}}$The weights are given by:w ₁(k)={[Σ+h ₂(k)h ₂(k)^(H)]⁻¹ h ₁(k)}/{h ₁(k)^(H) [Σ+h ₂(k)h₂(k)^(H)]⁻¹ h ₁(k)}w ₂(k)={[Σ+h ₁(k)h ₁(k)^(H)]⁻¹ h ₂(k)}/{h ₂(k)^(H) [Σ+h ₁(k)h₁(k)^(H)]⁻¹ h ₂(k)}where

${{w_{j}(k)} = {{\begin{bmatrix}w_{j,1} \\w_{j,2}\end{bmatrix}\mspace{14mu}{and}\mspace{14mu}\sum} = \begin{bmatrix}{\sigma_{1}^{2}(k)} & 0 \\0 & {\sigma_{2}^{2}(k)}\end{bmatrix}}},$the covariance of the AWGN noise

$\begin{bmatrix}{n_{1}(k)} \\{n_{2}(k)}\end{bmatrix}.$Note that the w_(j)(k) satisfy h_(j)(k)^(H)w_(j)(k)=1 and correspond tothe rows of detection matrix F(¹) of section 2. The corresponding SINRsare:SINR₁(k)=h ₁(k)^(H) [Σ+h ₂(k)h ₂(k)^(H)]⁻¹ h ₁(k)SINR₂(k)=h ₂(k)^(H) [Σ+h ₁(k)h ₁(k)^(H)]⁻¹ h ₂(k)where h₁(k)^(H) . . . h₁(k) relates to the signal power, Σ relates tothe AWGN noise power, and h₂(k) h₂(k)^(H) relates to the interferencepower in SINR₁(k); SINR₂(k) is analogous.

As illustrated in FIG. 3 b, implement the iterative detection withinterference cancellation by using a hard decision on the soft estimatewith the larger SNR. Without loss of generality, takez₁(k)=w₁(k)^(H)r(k) as having the larger SNR and let ŝ₁(k) be thecorresponding hard decision for s₁(k). Then cancel the signalregenerated from ŝ₁(k), and use this to re-estimate s₂(k). That is,define:r′(k)=r(k)−h ₁(k)ŝ ₁(k)and determine z′₂(k), a soft estimate for s₂(k), from thisinterference-cancelled signal byz′ ₂(k)=w ₃(k)^(H) r′(k)where the weights w₃(k) correspond to the interference cancelled signalin contrast to the weights w₂(k) which estimate s₂(k) from the signalincluding s₁(k) interference. Thus the detector output to thedemodulator for conditional probability computations would be z₁(k) andz′₂(k), together with the normalizations (scalings). And these softestimates may be unbiased as previously noted. In particular,preliminarily consider the case of no error in ŝ₁. This is equivalent tojust setting h₁(k)=0 in the foregoing expression for w₂(k); namely,w ₃(k)={Σ⁻¹ h ₂(k)}/{h ₂(k)^(H)Σ⁻¹ h ₂(k)}

The detector also supplies normalizations (scalings) γ₁ and γ₂ for z₁(k)and z′₂(k), respectively, to the demodulator for computation of theconditional probabilities (and branch metrics) for decoding. For γ₁ usethe noise variance scaling (reciprocal of SINR) analogous to that ofsection 2 and cited above:γ₁(k)=1/{h ₁(k)^(H) [Σ+h ₂(k)h ₂(k)^(H)]⁻¹ h ₁(k)}Note that this may also be expressed asw₁(k)^(H)[Σ+h₂(k)h₂(k)^(H)]w₁(k).

For γ₂(k) however, the preferred embodiments provide scalings whichaccount for the possibility of error in the hard decision used in theinterference cancellation. Indeed, the two symbol streams have beenencoded with an error-correcting code (FEC in FIGS. 2 a, 3 a), and sothe decoding may actually correct an erroneous hard decision ŝ₁ used inthe interference cancellation.

As illustrated in FIG. 1, the first preferred embodiment detectors andmethods compensate for this possibility of decision error in theinterference cancellation by including a term proportional to themagnitude of detecting a symbol of the first stream as a symbol of thesecond stream (essentially the inner product of h₁ with h₂) as follows:γ₂(k)=w ₃(k)^(H) Σw ₃(k)+α(k)|w ₃(k)^(H) h ₁(k)|²The first preferred embodiment methods take the proportionalityparameter α(k) equal to E[|s₁(k)−ŝ₁(k)|²]; so α explicitly depends uponthe likelihood of a decision error. Note when α=0 the scaling reducesto:

$\begin{matrix}{{\gamma_{2}(k)} = {{w_{3}(k)}^{H}{\sum\;{w_{3}(k)}}}} \\{= {1/\left\{ {{h_{2}(k)}^{H}{\sum\limits^{- 1}{h_{2}(k)}}} \right\}}} \\{= {1/\left\{ {{{{h_{21}(k)}}^{2}/{\sigma_{1}(k)}^{2}} + {{{h_{22}(k)}}^{2}/{\sigma_{2}(k)}^{2}}} \right\}}}\end{matrix}$which just demonstrates that with no interference 1/γ₂ is the sum of theSNRs of the two subchannels from transmitter antenna 2 to the tworeceiver antennas for the kth tone.

In general, α=E[|s₁−ŝ₁|²] can be evaluated for AWGN channels. Forexample, presume a simple symbol constellation, BPSK, with two possiblesymbols: −1 and +1. In this case the two Gaussian exponents, (z₁±1)²/γ₁,simplify to ±2z₁/γ₁ plus common terms which factor out and cancel. Thusthe probability of a decision error from soft estimate z₁ becomes:

p(ŝ₁ ≠ s₁❘z₁) = exp (−z₁/γ₁)/{exp (−z₁/γ₁) + exp (z₁/γ₁)}          = [1 − tanh (z₁/γ₁)]/2And so α=2²p(ŝ₁≠s₁|z₁)=2[1−tan h(−|z₁|/γ₁)] because |s₁−ŝ₁|=2 when ŝ₁≠s₁and equals 0 otherwise. Hence, for BPSK the scaling becomes:

γ₂(k) = w₃(k)^(H)∑w₃(k) + 4p(ŝ₁ ≠ s₁❘z₁)w₃(k)^(H)h₁(k)²     = w₃(k)^(H)∑w₃(k) + 2[1 − tanh (z₁/γ₁)]w₃(k)^(H)h₁(k)²For other symbol constellations the computations are more involved.

Further, the first preferred embodiments allow for over-estimation ofthe probability of decision error by inserting a positive weightingfactor λ into the tan h and thereby usep(ŝ ₁ ≠s ₁ |z ₁)=[1−tan h(λ|z ₁|γ₁)]/2in γ₂(k). A positive λ less than 1 makes the tan h smaller and thusincreases the probability estimate and consequent interference errorcompensation.

FIG. 4 shows simulation results of frame error rate as a function oftransmit SNR, E_(s)/N₀, for a coding rate of ¾, QPSK modulation,200-byte packets, and three path Rayleigh fading. The figure includesthis first preferred embodiment compensation method together with alower bound on frame error rate which takes α(k)=0 when there is nodecision error and sets α(k) to the interference power when there is adecision error. FIG. 4 also shows the frame error rate for the secondand third preferred embodiments described in the following section.

4. Further 2×2 Preferred Embodiment Scalings

Again consider an interference cancellation 2×2 OFDM system as in theforegoing section 3. Second and third preferred embodiment detectors andmethods of compensation for decision error in the cancellation alsoapply to the parameter α(k) in the scaling for the second detectedsymbol:γ₂(k)=w ₃(k)^(H) Σw ₃(k)+α(k)|w ₃(k)^(H) h ₁(k)|²The second preferred embodiments take α=1/(β+SINR₁(k)) where β is apositive constant. This α depends upon the likelihood of decision errorin that as SINR₁(k) increases the probability of decision error in ŝ₁decreases; and this α can also account for the case where SINR₂(k)approaches 0. In particular, the choice of β=1 is intuitively appealingas 1/(1+SINR) also is proportional to the probability of error in aRayleigh fading environment. This choice of α has low computationalcomplexity because SINR₁(k) was already evaluated for the selection ofwhich of the two symbols to estimate first and use to regenerate thecancellation signal.

A third preferred embodiment also uses α=1/(β+SINR) as in the secondpreferred embodiment but simplifies the computation by replacing theSINR₁(k) with the decorrelator SINR given by

${{SINR}_{1}(k)} = \frac{{{{h_{1}(k)}}^{2}{{h_{2}(k)}}^{2}} - {{{h_{1}^{H}(k)}{h_{2}(k)}}}^{2}}{{{h_{2}(k)}}^{2}}$This replacement relies on the observation that for small AWGN (i.e.,small σ_(j)(k)) the SINR₁(k) is close to the decorrelator SINR. In sucha case, with β=1, the scaling essentially is the inverse of SINR₂(k):γ₂(k)=1/{h ₂(k)^(H) [Σ+h ₁(k)h ₁(k)^(H)]⁻¹ h ₂(k)}

FIG. 4 simulations compare the first preferred embodiment methods withthe second and third preferred embodiment methods for β=1.

5. Modifications

For systems with more than two antennas and symbol streams, thecancellation error compensation methods may be extended and even mixed.For example, if z₁(k), z₂(k), and z₃(k) are detected in this order, thensymbol ŝ₁(k) is detected in the first iteration. The received signal dueto ŝ₁(k) is then regenerated and subtracted from r(k) to give r′(k) andz′₂(k) (and z′₃(k)) are detected from r′(k) together with scaling forz′₂(k) which incorporates an ŝ₁(k) error statistic. Then obtain ŝ₂(k)from z′₂(k); this constitutes the second iteration. Finally, thecontribution due to both ŝ₁(k) and ŝ₂(k) is taken out from the receivedsignal to have r″(k) and z″₃(k) is detected from this together with ascaling which incorporates an ŝ₁(k) error and/or an ŝ₂(k) errorstatistic. The ŝ₁(k) error and/or ŝ₂(k) error statistic could differfrom the ŝ₁(k) error statistic used with the scaling for z′₂(k).

1. A method of detecting in a receiver, comprising: (a) receiving aQ-vector signal by the receiver representing a set of P symbols where Pand Q are both integers greater than 1; (b) estimating a first symbol ofsaid set of P symbols; (c) subtracting an estimate of the portion ofsaid received signal due to said first symbol estimate from step (b) togive a first interference-cancelled received signal; (d) soft-estimatinga second symbol of said set of P symbols from said firstinterference-cancelled received signal; and e) providing a scaling forsaid soft-estimated second symbol from step (d) as a combination of (i)a detection scaling for said second symbol using said firstinterference-cancelled received signal and (ii) a first symbol estimateerror term wherein said first symbol estimate error term includes astatistic relating to error in said first symbol estimate.
 2. The methodof claim 1, wherein: (a) each of said P symbol is a vector of componentswith each component an element of a constellation where the number ofcomponents is greater than
 1. 3. The method of claim 2, wherein: (a)P=Q=2; and (b) said components of each of said symbols correspond totones of an orthogonal frequency division multiplex system with K toneswhere K is an integer greater than
 1. 4. The method of claim 1, furthercomprising: (a) estimating said second symbol of said set of P symbols;(b) subtracting an estimate of the portion of said firstinterference-cancelled received signal due to said second symbolestimate from step (a) to give a second interference-cancelled receivedsignal; (c) soft-estimating a third symbol of said set of P symbols fromsaid second interference-cancelled received signal; and (d) providing ascaling for said soft-estimated third symbol from step (c) as acombination of (i) a detection scaling for said third symbol using saidsecond interference-cancelled received signal and (ii) a first symbolestimate error and/or second symbol estimate error term wherein saidfirst symbol estimate error and/or second symbol estimate error termincludes a statistic relating to error in said first symbol estimateand/or said second symbol estimate.
 5. The method of claim 1, wherein:(a) said first symbol error term is α|w^(H)h₁|² where w is a Q-vector ofdetection weights for soft-estimating said second symbol from said firstinterference-cancelled received signal, h₁s₁ is an estimate of theportion of said received signal due to said first symbol estimate whenS₁ is said first symbol estimate, h₁ is a channel effect for s₁, and αrelates to error in said first symbol estimate.
 6. The method of claim5, wherein: (a) α equals the expectation of |s₁−ŝ₁|² where s₁is saidfirst symbol and ŝ₁ is said first symbol estimate.
 7. The method ofclaim 5, wherein: (a) αequals 1/(β+SINR₁) where β is a positive numberand SINR₁) is the estimated signal to interference plus noise ratio ofsaid first symbol.
 8. The method of claim 5, wherein: (a) α equals1/(β+SINR₁) where β is a positive number and SINR₁ is the estimateddecorrelator signal to interference plus noise ratio.
 9. The method ofclaim 1, wherein: (a) said soft-estimated second symbol from step (d) ofclaim 1 is minimum mean squared error estimation.
 10. The method ofclaim 1, wherein: (a) said soft-estimated second symbol from step (d) ofclaim 1 is zero-forcing estimation.
 11. An iterative detector for areceiver, comprising: (a) a first detector for estimating a first symbolfrom a received Q-vector signal by the receiver representing a set of Psymbols where P and Q are both integers greater than 1; (b) aregenerator-subtracter coupled to said first detector and for (i)regenerating an estimate of the portion of said received signal due to afirst symbol estimate from said first detector and (ii) subtracting thisregenerated estimate from said received signal to give a firstinterference-cancelled received signal; (c) a second detector coupled tosaid regenerator-subtractor and for soft-estimating a second symbol ofsaid set of P symbols from said first interference-cancelled receivedsignal; and (d) a scaling circuit coupled to said second detector andfor scaling a soft-estimated second symbol from said second detector,wherein said scaling circuit combines (i) a detection scaling for saidsecond detector and (ii) a first symbol estimate error term wherein saidfirst symbol estimate error term includes a statistic relating to errorin said first symbol estimate.
 12. The detector of claim 11, wherein:(a) said first detector, said regenerator-subtractor, said seconddetector, and said scaling circuit are implemented as a programmableprocessor plus program memory plus peripheral circuitry.
 13. Thedetector of claim 11, wherein: (a) said first detector outputs a softestimate of said first symbol to said scaling circuit; and (b) saidscaling circuit outputs soft estimates and scalings for both said firstsymbol and said second symbol to a decoder.
 14. The detector of claim11, wherein: (a) P=Q=2; and (b) said components of each of said symbolscorrespond to tones of an orthogonal frequency division multiplex systemwith K tones.
 15. The detector of claim 14, further comprising: (a) adiscrete Fourier transform circuit coupled to said first detector andsaid regenerator-subtractor, said discrete Fourier transform circuit forK -point Fourier transforms.
 16. The detector of claim 11, wherein: (a)said first symbol error term of said scaling circuit is α|w^(H)h₁|²where w is a Q-vector of detection weights for soft-estimating saidsecond symbol from said first interference-cancelled received signal,h₁s₁ is an estimate of the portion of said received signal due to saidfirst symbol estimate when s₁ is said first symbol estimate, h₁ is achannel effect s₁, and α relates to error in said first symbol estimate.17. The detector of claim 16, wherein: (a) α equals the expectation of|s₁−ŝ₁|² where s₁is said first symbol and ŝ₁is said first symbolestimate.
 18. The detector of claim 16, wherein: (a) α equals1/(β+SINR₁) where β is a positive number and SINR₁) is the estimatedsignal to interference plus noise ratio of said first symbol.
 19. Thedetector of claim 16, wherein: (a) α equals 1/(β+SINR₁) where β is apositive number and SINR₁ is the estimated decorrelator signal tointerference plus noise ratio.
 20. The detector of claim 11, wherein:(a) said soft-estimated second symbol of said second detector is aminimum mean squared error estimator.